We focus on the control of unknown partial differential equations (PDEs). The system dynamics is unknown, but we assume we are able to observe its evolution for a given control input, as typical in a reinforcement learning framework. We propose an algorithm based on the idea to control and identify on the fly the unknown system configuration. In this work, the control is based on the state-dependent Riccati approach, whereas the identification of the model on Bayesian linear regression. At each iteration, based on the observed data, we obtain an estimate of the a-priori unknown parameter configuration of the PDE and then we compute the control of the correspondent model. We show by numerical evidence the convergence of the method for infinite horizon control problems.

我们专注于未知偏微分方程（PDE）的控制。系统动力学是未知的，但我们假设我们能够观察给定控制输入的演化，就像强化学习框架中的典型情况一样。我们提出了一种基于动态控制和识别未知系统配置的思想的算法。在这项工作中，控制基于状态相关的 Riccati 方法，而模型的识别基于贝叶斯线性回归。在每次迭代中，根据观测到的数据，我们获得偏微分方程的先验未知参数配置的估计，然后计算相应模型的控制。我们通过数值证据证明了该方法对于无限视野控制问题的收敛性。